AI 中文总结
该研究将“别处效应”重新解释为程序不一致的校正，证明二元检验对其鲁棒，峰搜索需显式校正，并通过ATLAS希格斯搜索的试验因子，说明二者显著性的对应关系，为粒子物理显著性宣称提供更连贯框架。
AI 中文摘要
在粒子物理学中，发现宣称通常要求观测显著性超过5σ。然而，对5σ结果的解释关键取决于检验程序，即该假设是在参数空间中单个预先指定的点进行检验，还是通过扫描一系列可能的信号位置进行检验。这种区分产生了“别处效应”，这一概念被广泛使用但常被简单理解为对扫描的惩罚。在本研究中，我们将“别处效应”重新解释为对程序不一致的校正，这种不一致产生于在一种程序下生成零分布，而在另一种程序下计算检验统计量的情况。在假设检验框架内，我们研究其含义，阐明“别处效应”在二元检验和峰搜索场景中的不同作用。特别地，我们证明二元检验对“别处效应”具有鲁棒性，而峰搜索需要对信号位置的搜索进行显式校正。利用从ATLAS希格斯玻色子搜索校准得到的约26的中等试验因子，我们表明，对于相同的观测检验统计量值，峰搜索的3σ全局显著性可对应二元检验的约4σ显著性。这种重新表述为“别处效应”提供了更清晰的统计解释，并为理解粒子物理学中的显著性宣称提供了更连贯的框架。
英文摘要
In particle physics, discovery claims conventionally require an observed significance exceeding $5σ$. However, the interpretation of a $5σ$ result depends critically on the testing procedure, namely whether the hypothesis is tested at a single pre-specified point in parameter space or by scanning over a range of possible signal locations. This distinction gives rise to the look-elsewhere effect, a concept that is widely used but often interpreted as a simple penalty for scanning. In this work, we reinterpret the look-elsewhere effect as a correction for procedural inconsistency arising when the null distribution is generated under one procedure while the test statistic is evaluated under another. Within the framework of hypothesis testing, we examine its implications and clarify the distinct roles of the look-elsewhere effect in binary and peak-search scenarios. In particular, we show that binary test is robust against the look-elsewhere effect, whereas peak searches require an explicit correction for the search over signal locations. Using a moderate trial factor of approximately 26, calibrated from the ATLAS Higgs search, we show that a $3σ$ global significance of peak search can correspond to approximately $4σ$ significance of the binary test for the same value of the observed test statistic. This reformulation provides a clearer statistical interpretation of the look-elsewhere effect and offers a more coherent framework for understanding significance claims in particle physics.
Comments19 pages, 6 figures
